How persuaded are you? A typology of responses

Abstract

Several recent studies have suggested that there are two different ways in which a person can proceed when assessing the persuasiveness of a mathematical argument: by evaluating whether it is personally convincing, or by evaluating whether it is publicly acceptable. In this paper, using Toulmin's (1958) argumentation scheme, we produce a more detailed theoretical classification of the ways in which participants can interpret a request to assess the persuasiveness of an argument. We suggest that there are (at least) five ways in which such a question can be interpreted. The classification is illustrated with data from a study that asked undergraduate students and research-active mathematicians to rate how persuasive they found a given argument. We conclude by arguing that researchers interested in mathematical conviction and proof validation need to be aware of the different ways in which participants can interpret questions about the persuasiveness of arguments, and that they must carefully control for these variations during their studies.

Keywords:

• arguments
• persuasion
• proof

Acknowledgements

We are grateful to Janet Ainley, Paola Iannone, Andreas Moutsios-Rentzos, Dave Pratt and Keith Weber for helpful comments on earlier drafts of this manuscript.

Notes

1. Toulmin's (1958) use of the word ‘warrant’ is not identical to the way in which the term has been used by some mathematics education literature. Rodd (2000), for example, saw a warrant as removing uncertainty, whereas Toulmin was more flexible, accepting that a warrant can be qualified so as to merely reduce uncertainty.

2. Elena Nardi has pointed out to us that this may be the type of persuasion enlisted by propagandists who use sensationalist data in the hope that the affinity of the audience for these data will sway them to support whatever conclusion he or she wishes to draw.